## Precalculus Practice Exam

Part 1 Test 2 Time: 1 hour

1. If and g(x)=x-1, let h(x)=f(g(x)).
• Find h(x).
• What is the domain of h(x)?
• Find h(2) and h(0).

Answers: The function , with interval of domain . h(2)=1, and h(0) is undefined.

2. Let A=(3,1), B=(7,-4) and C=(10,9).
• Find an equation of the line passing through the points A and B.
• Find an equation of the line parallel to the line in the first part that passes through the point C.
• Find an equation of the line perpendicular to the line in the first part that passes through the point B.

Answers: An equation for the first line is

for the second line

and for the third line

3. What is the vertex of the graph of the parabola ? Also: Describe how you would translate the graph so that the vertex is moved to the origin.

Answers: The vertex is located at . To move the vertex to the origin, you have to shift up by units and to the left by units.

• Solve the equation .

Answers: The equation has the solutions x=0, x=-1 and x=4. The inequality has at its solution set the union of the intervals and .

4. A chemist mixes a 12% hydrochloric acid solution with a 5% hydrochloric acid solution. How many milliliters of each solution should the chemist use to make a 500 ml liter solution that is 8% hydrochloric acid?

Answer: The exact answer is ml of the 12% solution and ml of the 5% solution. The approximate answer is 214.29 ml of the 12% solution and 285.71 ml of the 5% solution.

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Thu Jun 12 22:58:04 MDT 1997